Railway Operations Research Seminar ‘Put Passengers First’ May 3, 2016, Leuven Performance-based railway timetabling Integrating timetable construction and evaluation 3 May 2016 Rob M.P. Goverde Department of Transport and Planning Delft University of Technology r.m.p.goverde@tudelft.nl Performance-based railway timetabling 1
Outline Performance-based railway timetabling • Introduction • Timetable performance indicators • Timetabling design levels • Three-level timetabling framework • Case study • Conclusions Performance-based railway timetabling 2
Introduction Current practice and challenge Current practice • Timetable construction either macroscopic using normative input or microscopic on corridors without network focus • Timetable evaluation either lacking or by simulation after timetable construction without clear feedback to timetable design • No well-defined timetable performance indicators Challenge (ON-TIME project) • Performance-based railway timetabling Define timetable performance indicators Optimize timetable with respect to these performance indicators Performance-based railway timetabling 3
Timetable performance indicators Timetable performance indicators • Travel time efficiency Short travel times between any OD pair, incl. running/dwell/transfer times • Infrastructure occupation Time required for a given timetable pattern on a given infrastructure • Stability Sufficient time allowances to settle delays • Feasibility Realizability: all processes realizable within their scheduled process times Conflict-freeness: scheduled train paths are conflict free • Robustness Delay propagation behaviour kept within bounds • Energy-efficiency Timetable allows energy-efficient train operations Performance-based railway timetabling 4
Timetable peformance indicators Headway and blocking times • Minimum headway distance between successive trains CIE4872: Automatic block signalling 5
Timetable peformance indicators Headway and blocking times 𝑚 𝑡𝑗ℎ𝑢 𝑚 𝑑𝑚𝑓𝑏𝑠 𝑚 𝑡𝑓𝑢𝑣𝑞 𝑚 𝑠𝑓𝑚𝑓𝑏𝑡𝑓 𝑚 𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ 𝑚 𝑐𝑚𝑝𝑑𝑙 R G Y 𝐼 𝑛𝑗𝑜 • Minimum headway distance between successive trains 𝐼 𝑛𝑗𝑜 = 𝑚 𝑡𝑓𝑢𝑣𝑞 + 𝑚 𝑡𝑗ℎ𝑢 + 𝑚 𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ + 𝑚 𝑐𝑚𝑝𝑑𝑙 + 𝑚 𝑑𝑚𝑓𝑏𝑠 + 𝑚 𝑠𝑓𝑚𝑓𝑏𝑡𝑓 Distance over time to setup the route and clear signal 𝑚 𝑡𝑓𝑢𝑣𝑞 • 𝑚 𝑡𝑗ℎ𝑢 Sight distance to approach signal • 𝑚 𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ Distance approach signal to main signal (block length) • 𝑚 𝑐𝑚𝑝𝑑𝑙 Block length • 𝑚 𝑑𝑚𝑓𝑏𝑠 Clearing distance over train length and overlap • 𝑚 𝑠𝑓𝑚𝑓𝑏𝑡𝑓 Distance over time to release the block • CIE4872: Automatic block signalling 6
Timetable peformance indicators Headway and blocking times 𝑚 𝑡𝑗ℎ𝑢 𝑚 𝑑𝑚𝑓𝑏𝑠 𝑚 𝑠𝑓𝑚𝑓𝑏𝑡𝑓 𝑚 𝑡𝑓𝑢𝑣𝑞 Distance 𝑚 𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ 𝑚 𝑐𝑚𝑝𝑑𝑙 Time Setup time Sight and reaction time Approach time Blocking time Occupation time 𝑈 𝑐𝑚𝑝𝑑𝑙 = 𝑢 𝑡𝑓𝑢𝑣𝑞 + 𝑢 𝑡𝑗ℎ𝑢 + 𝑢 𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ + 𝑢 𝑐𝑚𝑝𝑑𝑙 + 𝑢 𝑑𝑚𝑓𝑏𝑠 + 𝑢 𝑠𝑓𝑚𝑓𝑏𝑡𝑓 Running time Clearing time Release time CIE4872: Automatic block signalling 7
Timetable performance indicators Stations , signals Time Performance-based railway timetabling 8
Timetable performance indicators Distance Distance Time Time Performance-based railway timetabling 9
Timetable design levels Macroscopic (Normative) IT 1 FR 0 Stable (Partially) unplanned NL UK Deterministic Stochastic SE DE CH 2 3 4 Conflict-free Robust Resilient Microscopic (incl. traffic control) Performance-based railway timetabling 10
Timetabling design levels Clasification of the timetable design process Level 0: Low quality • No conflict detection or stability analysis Level 1: Stable timetable • Main characteristic: stability analysis Level 2: Feasible (or conflict-free) timetable • Main characteristic: conflict detection ánd stability analysis Level 3: Robust timetable • Main characteristic: robustness analysis (and stability and feasibility) Level 4: Resilient timetable • Main characteristic: integration of timetabling and traffic control Proof that a robust timetable exists in combination with traffic management; parts of the final timetable may be computed in real- time when actual circumstances are known (delays, freight paths) Performance-based railway timetabling 11
Timetabling design levels Clasification of the timetable design process • Higher level requires more information and advanced tools in the timetable design process • Workload of dispatchers depends on timetable design level Level 0 : Much work to do for traffic control (or low punctuality) Level 1 : Traffic control must solve structural conflicts Level 2 : Traffic control must monitor and solve small delays Level 3 : Little work for traffic control unless large delays or disruptions Level 4 : Advanced decision support to solve disturbances and delays • Different parts in a network may require different approach (level) Capacity bottlenecks Focus on resilience, example: Schiphol Low traffic lines Focus on stability Performance-based railway timetabling 12
Three-level timetabling framework … for performance -based railway timetabling railML Macroscopic Microscopic Fine-Tuning MacroTT EE-profiles Module Module Module ● Efficiency ● Feasibility ● Energy efficiency ● Robustness ● Stability ● Robustness • Process time bounds • Bandwidths • Minimum headways Feasible? NO YES Stable? NO YES TRC 2016 Performance-based railway timetabling 13
Three-level timetabling framework Timetabling levels Microscopic (track section level) • Speed and running time computations incl. time supplements • Conflict detection using blocking times • Infrastructure occupation & stability tests by compression method • Constraints tightening or relaxation for macroscopic model input Macroscopic (network level) • Trade-off between minimal travel times and maximal robustness • Also minimizing missed connections and cancelled train paths • Timetable precision of 5 s minimizing capacity waste Fine-tuning (corridor level) • Energy-efficient speed profiles using optimal control • Stochastic optimization of time allowances for local trains Performance-based railway timetabling 14
Macroscopic model Integer Linear Program and delay propagation • Least-cost path problem over a time-extended graph (ILP) • Solved by randomized multi-start greedy heuristic that iteratively schedules trains using a dynamic programming subroutine • Robust cost includes mean settling time from Monte Carlo delay propagation of stochastic initial delays TRB 2016 Performance-based railway timetabling 15
Microscopic models Dealing with running time supplements Reduced cruising speed Time-minimal Energy-optimal 140 120 100 Speed [km/h] 80 60 40 20 0 0 1 2 3 4 5 6 7 8 Distance [m] 4 x 10 Ut Ht Ehv • Time-minimal, non-coasting and energy-efficient speed profiles Performance-based railway timetabling 16
Corridor fine-tuning Trade-off: time allowance in dwell or running time TRC 2016 Performance-based railway timetabling 17
Corridor fine-tuning Multi-stage multi-objective dynamic programming TRC 2016 Performance-based railway timetabling 18
Corridor fine-tuning Multi-stage multi-objective dynamic progamming Cost criteria at each stop (arrival/departure stage) 𝒋 • Expected energy consumption until target station at stage 𝑗 • Expected delay at target station from stage 𝑗 • Expected total delay at intermediate stops from stage 𝑗 • Each cost at stage 𝑗 depends on the time allowance decision at stage 𝑗 • Each cost at stage 𝑗 is a recursive equation in the cost at stage 𝑗 + 1 Dynamic programming solution approach • Solve recursions backwards from target station back to begin • At each stage find the optimal time allowance at that stage that minimizes a weighted squared sum of the three cost criteria at that stage Performance-based railway timetabling 19
Case study Dutch network around ’s Hertogenbosch • Infrastructure and line plan 2012 • Two intersecting corridors Utrecht-Eindhoven and Tilburg-Nijmegen • Hourly timetable pattern with 2 x 8 ICs per hr 2 x 10 local trains per hr One freight path (Ut-Ehv) Many transfers in ‘s Hertogenbosch (and elsewhere) Performance-based railway timetabling 20
Case study Microscopic and macroscopic models Timetable design norms Min running time supplement 5% Max running time supplement 30% Max journey time extension 20% Dwell time at short stops 35 s Dwell time at macro points 1- 2’ Min transfer times 1- 3’ Microscopic network Macro network 1000 nodes, 1500 arcs 14 nodes and 14 arcs Performance-based railway timetabling 21
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